How can you use trigonometric functions to simplify $26 e^{\frac{π}{2} i}$ $26 e^( ( pi)/2 i )$ into a non-exponential complex number?

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Answer 1 · 2016-04-11T09:43:32

$26 i$ $26i$

$ρ e^{θ i} = ρ cos (θ) + ρ i sin (θ)$ $color(blue)(rhoe^(thetai)=rhocos(theta)+rhoisin(theta))$

$26 e^{(\frac{π}{2}) i} = 26 cos (\frac{π}{2}) + 26 i sin (\frac{π}{2})$ $26e^((pi/2)i)=26cos(pi/2)+26isin(pi/2)$

$= 26 \cdot 0 + 26 i \cdot 1 = 26 i$ $=26*0+26i*1=26i$

How can you use trigonometric functions to simplify 26eπ2i 26 e^( ( pi)/2 i ) into a non-exponential complex number?